Implements D = - inv(C) * N for a variable reduction projection. More...

#include <ConstrainedOptPack_MatrixVarReductImplicit.hpp>

Inheritance diagram for ConstrainedOptPack::MatrixVarReductImplicit:

Private Types
typedef std::vector < VectorSpace::vec_mut_ptr_t >	InvCtN_rows_t

typedef std::list< index_type >	InvCtN_rows_set_list_t

Private Member Functions
void	assert_initialized () const

Private Attributes
AbstractLinAlgPack::MatrixOpNonsing *	C

AbstractLinAlgPack::MatrixOp *	N

AbstractLinAlgPack::MatrixOp *	D_direct

Public types
typedef Teuchos::RCP< const MatrixOpNonsing >	mat_nonsing_ptr_t

typedef Teuchos::RCP< const MatrixOp >	mat_ptr_t

Constructors / initializers
virtual void	initialize (const mat_nonsing_ptr_t &C, const mat_ptr_t &N, const mat_ptr_t &D_direct)
	Initialize `this` matrix object. More...

virtual void	set_uninitialized ()
	Set the matrix to uninitialized. More...

Access
const mat_nonsing_ptr_t &	C_ptr () const
	Return the smart pointer to the aggregate basis matrix object `C`. More...

const mat_ptr_t &	N_ptr () const
	Return the smart pointer to the aggregate nonbasis matrix object `N`. More...

const mat_ptr_t &	D_direct_ptr () const
	Return the smart pointer to the aggregate precomputed matrix object `D_direct` (if set). More...

Overridden from MatrixBase.
size_type	rows () const

size_type	cols () const

Overridden from MatrixOp.
const VectorSpace &	space_cols () const

const VectorSpace &	space_rows () const

MatrixOp &	operator= (const MatrixOp &M)

std::ostream &	output (std::ostream &) const

void	Vp_StMtV (VectorMutable *v_lhs, value_type alpha, BLAS_Cpp::Transp trans_rhs1, const Vector &v_rhs2, value_type beta) const

void	Vp_StMtV (VectorMutable *v_lhs, value_type alpha, BLAS_Cpp::Transp trans_rhs1, const SpVectorSlice &sv_rhs2, value_type beta) const

void	Vp_StPtMtV (VectorMutable *v_lhs, value_type alpha, const GenPermMatrixSlice &P_rhs1, BLAS_Cpp::Transp P_rhs1_trans, BLAS_Cpp::Transp M_rhs2_trans, const Vector &v_rhs3, value_type beta) const

void	Vp_StPtMtV (VectorMutable *v_lhs, value_type alpha, const GenPermMatrixSlice &P_rhs1, BLAS_Cpp::Transp P_rhs1_trans, BLAS_Cpp::Transp M_rhs2_trans, const SpVectorSlice &sv_rhs3, value_type beta) const

Additional Inherited Members
Public Types inherited from AbstractLinAlgPack::MatrixOp
enum	EMatNormType { MAT_NORM_INF, MAT_NORM_2, MAT_NORM_1, MAT_NORM_FORB }
	Type of matrix norm. More...

Public Member Functions inherited from AbstractLinAlgPack::MatrixOp
virtual void	zero_out ()
	M_lhs = 0 : Zero out the matrix. More...

virtual void	Mt_S (value_type alpha)
	M_lhs *= alpha : Multiply a matrix by a scalar. More...

virtual MatrixOp &	operator= (const MatrixOp &mwo_rhs)
	M_lhs = mwo_rhs : Virtual assignment operator. More...

virtual mat_mut_ptr_t	clone ()
	Clone the non-const matrix object (if supported). More...

virtual mat_ptr_t	clone () const
	Clone the const matrix object (if supported). More...

const MatNorm	calc_norm (EMatNormType requested_norm_type=MAT_NORM_1, bool allow_replacement=false) const
	Compute a norm of this matrix. More...

virtual mat_ptr_t	sub_view (const Range1D &row_rng, const Range1D &col_rng) const
	Create a transient constant sub-matrix view of this matrix (if supported). More...

mat_ptr_t	sub_view (const index_type &rl, const index_type &ru, const index_type &cl, const index_type &cu) const
	Inlined implementation calls `this->sub_view(Range1D(rl,ru),Range1D(cl,cu))`. More...

virtual mat_ptr_t	perm_view (const Permutation P_row, const index_type row_part[], int num_row_part, const Permutation P_col, const index_type col_part[], int num_col_part) const
	Create a permuted view: `M_perm = P_row' * M * P_col`. More...

virtual mat_ptr_t	perm_view_update (const Permutation P_row, const index_type row_part[], int num_row_part, const Permutation P_col, const index_type col_part[], int num_col_part, const mat_ptr_t &perm_view) const
	Reinitialize a permuted view: `M_perm = P_row' * M * P_col`. More...

Public Member Functions inherited from AbstractLinAlgPack::MatrixBase
virtual	~MatrixBase ()
	Virtual destructor. More...

virtual size_type	nz () const
	Return the number of nonzero elements in the matrix. More...

Protected Member Functions inherited from AbstractLinAlgPack::MatrixOp
virtual bool	Mp_StM (MatrixOp *mwo_lhs, value_type alpha, BLAS_Cpp::Transp trans_rhs) const
	mwo_lhs += alpha * op(M_rhs) (BLAS xAXPY). More...

virtual bool	Mp_StM (value_type alpha, const MatrixOp &M_rhs, BLAS_Cpp::Transp trans_rhs)
	M_lhs += alpha * op(mwo_rhs) (BLAS xAXPY). More...

virtual bool	Mp_StMtP (MatrixOp *mwo_lhs, value_type alpha, BLAS_Cpp::Transp M_trans, const GenPermMatrixSlice &P_rhs, BLAS_Cpp::Transp P_rhs_trans) const
	mwo_lhs += alpha * op(M_rhs) * op(P_rhs). More...

virtual bool	Mp_StMtP (value_type alpha, const MatrixOp &mwo_rhs, BLAS_Cpp::Transp M_trans, const GenPermMatrixSlice &P_rhs, BLAS_Cpp::Transp P_rhs_trans)
	M_lhs += alpha * op(mwo_rhs) * op(P_rhs). More...

virtual bool	Mp_StPtM (MatrixOp *mwo_lhs, value_type alpha, const GenPermMatrixSlice &P_rhs, BLAS_Cpp::Transp P_rhs_trans, BLAS_Cpp::Transp M_trans) const
	mwo_lhs += alpha * op(P_rhs) * op(M_rhs). More...

virtual bool	Mp_StPtM (value_type alpha, const GenPermMatrixSlice &P_rhs, BLAS_Cpp::Transp P_rhs_trans, const MatrixOp &mwo_rhs, BLAS_Cpp::Transp M_trans)
	M_lhs += alpha * op(P_rhs) * op(mwo_rhs). More...

virtual bool	Mp_StPtMtP (MatrixOp *mwo_lhs, value_type alpha, const GenPermMatrixSlice &P_rhs1, BLAS_Cpp::Transp P_rhs1_trans, BLAS_Cpp::Transp M_trans, const GenPermMatrixSlice &P_rhs2, BLAS_Cpp::Transp P_rhs2_trans) const
	mwo_lhs += alpha * op(P_rhs1) * op(M_rhs) * op(P_rhs2). More...

virtual bool	Mp_StPtMtP (value_type alpha, const GenPermMatrixSlice &P_rhs1, BLAS_Cpp::Transp P_rhs1_trans, const MatrixOp &mwo_rhs, BLAS_Cpp::Transp M_trans, const GenPermMatrixSlice &P_rhs2, BLAS_Cpp::Transp P_rhs2_trans)
	M_lhs += alpha * op(P_rhs1) * op(mwo_rhs) * op(P_rhs2). More...

virtual void	Vp_StMtV (VectorMutable *v_lhs, value_type alpha, BLAS_Cpp::Transp trans_rhs1, const Vector &v_rhs2, value_type beta) const =0
	v_lhs = alpha * op(M_rhs1) * v_rhs2 + beta * v_lhs (BLAS xGEMV) More...

virtual void	Vp_StMtV (VectorMutable *v_lhs, value_type alpha, BLAS_Cpp::Transp trans_rhs1, const SpVectorSlice &sv_rhs2, value_type beta) const
	v_lhs = alpha * op(M_rhs1) * sv_rhs2 + beta * v_lhs (BLAS xGEMV) More...

virtual void	Vp_StPtMtV (VectorMutable *v_lhs, value_type alpha, const GenPermMatrixSlice &P_rhs1, BLAS_Cpp::Transp P_rhs1_trans, BLAS_Cpp::Transp M_rhs2_trans, const Vector &v_rhs3, value_type beta) const
	v_lhs = alpha * op(P_rhs1) * op(M_rhs2) * v_rhs3 + beta * v_rhs More...

virtual void	Vp_StPtMtV (VectorMutable *v_lhs, value_type alpha, const GenPermMatrixSlice &P_rhs1, BLAS_Cpp::Transp P_rhs1_trans, BLAS_Cpp::Transp M_rhs2_trans, const SpVectorSlice &sv_rhs3, value_type beta) const
	v_lhs = alpha * op(P_rhs1) * op(M_rhs2) * sv_rhs3 + beta * v_rhs More...

virtual value_type	transVtMtV (const Vector &v_rhs1, BLAS_Cpp::Transp trans_rhs2, const Vector &v_rhs3) const
	result = v_rhs1' * op(M_rhs2) * v_rhs3 More...

virtual value_type	transVtMtV (const SpVectorSlice &sv_rhs1, BLAS_Cpp::Transp trans_rhs2, const SpVectorSlice &sv_rhs3) const
	result = sv_rhs1' * op(M_rhs2) * sv_rhs3 More...

virtual void	syr2k (BLAS_Cpp::Transp M_trans, value_type alpha, const GenPermMatrixSlice &P1, BLAS_Cpp::Transp P1_trans, const GenPermMatrixSlice &P2, BLAS_Cpp::Transp P2_trans, value_type beta, MatrixSymOp *symwo_lhs) const
	Perform a specialized rank-2k update of a dense symmetric matrix of the form: More...

virtual bool	Mp_StMtM (MatrixOp *mwo_lhs, value_type alpha, BLAS_Cpp::Transp trans_rhs1, const MatrixOp &mwo_rhs2, BLAS_Cpp::Transp trans_rhs2, value_type beta) const
	mwo_lhs = alpha * op(M_rhs1) * op(mwo_rhs2) + beta * mwo_lhs (left) (xGEMM). More...

virtual bool	Mp_StMtM (MatrixOp *mwo_lhs, value_type alpha, const MatrixOp &mwo_rhs1, BLAS_Cpp::Transp trans_rhs1, BLAS_Cpp::Transp trans_rhs2, value_type beta) const
	mwo_lhs = alpha * op(mwo_rhs1) * op(M_rhs2) + beta * mwo_lhs (right) (xGEMM) More...

virtual bool	Mp_StMtM (value_type alpha, const MatrixOp &mwo_rhs1, BLAS_Cpp::Transp trans_rhs1, const MatrixOp &mwo_rhs2, BLAS_Cpp::Transp trans_rhs2, value_type beta)
	M_lhs = alpha * op(mwo_rhs1) * op(mwo_rhs2) + beta * mwo_lhs (left) (xGEMM) More...

virtual bool	syrk (BLAS_Cpp::Transp M_trans, value_type alpha, value_type beta, MatrixSymOp *sym_lhs) const
	Perform a rank-k update of a symmetric matrix of the form: More...

virtual bool	syrk (const MatrixOp &mwo_rhs, BLAS_Cpp::Transp M_trans, value_type alpha, value_type beta)
	Perform a rank-k update of a symmetric matrix of the form: More...

Detailed Description

Implements D = - inv(C) * N for a variable reduction projection.

This class is used to implement an implicit matrix defined as

D = - inv(C) * N

The operations y = op(D)*x are implemented as:

 y = D * x
   = -inv(C) * (N * x)

 y = D' * x
   = - N' * (inv(C') * x)

This class also allows the client to set a precomputed matrix D_direct that represents D = -inv(C)*N that will be used to extract rows or columns or to implement operations involving GenPermMatrixSlice when convenient. One might ask why this subclass would even be used if D_direct was even available. The reason is that it may be cheaper to perform the sparse solve and matrix-vector multiplication with C and N than it is to use a dense precomputed matrix D_direct. Determining if this class is even useful when D_direct is availible must be determined at runtime using timing data (which can be very hard to do well in general).

This implementation is designed to deal efficiently with the case where matrix- vector multiplications will only be performed with subsets of rows of inv(C)*N or columns of N'inv(C'). This primarily affects two types of operations:




y = b*y + a[-N'inv(C')]*x (x is a SpVectorSlice object) 

 y = b*y + a*op(P)[-inv(C)*N]*x (P has few nonzeros, x is any vector)

when D_direct is not set then needed rows of inv(C)*N are generated on the fly (as abstract vectors) and stored away for later use. When this->initialize() is called then all of these computed rows are discarded and they must be generated again.

Definition at line 91 of file ConstrainedOptPack_MatrixVarReductImplicit.hpp.

Member Typedef Documentation

typedef Teuchos::RCP<const MatrixOpNonsing> ConstrainedOptPack::MatrixVarReductImplicit::mat_nonsing_ptr_t

Definition at line 100 of file ConstrainedOptPack_MatrixVarReductImplicit.hpp.

typedef Teuchos::RCP<const MatrixOp> ConstrainedOptPack::MatrixVarReductImplicit::mat_ptr_t

Definition at line 102 of file ConstrainedOptPack_MatrixVarReductImplicit.hpp.

typedef std::vector<VectorSpace::vec_mut_ptr_t> ConstrainedOptPack::MatrixVarReductImplicit::InvCtN_rows_t

private

Definition at line 240 of file ConstrainedOptPack_MatrixVarReductImplicit.hpp.

typedef std::list<index_type> ConstrainedOptPack::MatrixVarReductImplicit::InvCtN_rows_set_list_t

private

Definition at line 241 of file ConstrainedOptPack_MatrixVarReductImplicit.hpp.

Member Function Documentation

void ConstrainedOptPack::MatrixVarReductImplicit::initialize	(	const mat_nonsing_ptr_t &	C,
		const mat_ptr_t &	N,
		const mat_ptr_t &	D_direct
	)

virtual

Initialize this matrix object.

Parameters

C	[in] Nonsingular basis matrix object. This matrix object must not be altered while `this` is in use or until `this->initialize()` is called again.
N	[in] Genaral nonbasis matrix object. This matrix object must not be altered while `this` is in use or until `this->initialize()` is called again.
D_direct	[in] Matrix object for `D = -inv(C)*N` already computed. The matrix object `D_direct` will not be modifed by `this` and must not be altered while c\ this matrix object is in use or until `this->initialize()` is called again. `D_direct == NULL` is allowed and `this` matrix object will just have to do without. For most applications (except those using direct linear solvers for `C` and when `N` has many columns) `D_direct` should be set to `NULL` and should not be computed by the client (that is the whole purpose for this matrix class).

Preconditions:

C.get() != NULL (throw std::invalid_argument)
N.get() != NULL (throw std::invalid_argument)
[D_direct != NULL] D_direct->space_cols().is_compatible(C->space_cols()) == true && D_direct->space_rows().is_compatible(N->space_rows()) == true (throw VectorSpace::IncompatibleVectorSpaces)

Postconditions:

this->C_ptr().get() == C.get()
this->N_ptr().get() == N.get()
this->D_direct_ptr().get() == N.get()

Definition at line 197 of file ConstrainedOptPack_MatrixVarReductImplicit.cpp.

void ConstrainedOptPack::MatrixVarReductImplicit::set_uninitialized ( )

virtual

Set the matrix to uninitialized.

Postconditions:

this->C_ptr().get() == NULL
this->N_ptr().get() == NULL
this->D_direct_ptr().get() == NULL

Definition at line 239 of file ConstrainedOptPack_MatrixVarReductImplicit.cpp.

const MatrixVarReductImplicit::mat_nonsing_ptr_t & ConstrainedOptPack::MatrixVarReductImplicit::C_ptr ( ) const

inline

Return the smart pointer to the aggregate basis matrix object C.

If this is the only reference to this matrix object, then return.count() == 1 will be true.

Definition at line 284 of file ConstrainedOptPack_MatrixVarReductImplicit.hpp.

const MatrixVarReductImplicit::mat_ptr_t & ConstrainedOptPack::MatrixVarReductImplicit::N_ptr ( ) const

inline

Return the smart pointer to the aggregate nonbasis matrix object N.

If this is the only reference to this matrix object, then return.count() == 1 will be true.

Definition at line 291 of file ConstrainedOptPack_MatrixVarReductImplicit.hpp.

const MatrixVarReductImplicit::mat_ptr_t & ConstrainedOptPack::MatrixVarReductImplicit::D_direct_ptr ( ) const

inline

Return the smart pointer to the aggregate precomputed matrix object D_direct (if set).

If this is the only reference to this matrix object, then return.count() == 1 will be true.

Definition at line 298 of file ConstrainedOptPack_MatrixVarReductImplicit.hpp.

size_type ConstrainedOptPack::MatrixVarReductImplicit::rows ( ) const

virtual

Reimplemented from AbstractLinAlgPack::MatrixBase.

Definition at line 249 of file ConstrainedOptPack_MatrixVarReductImplicit.cpp.

size_type ConstrainedOptPack::MatrixVarReductImplicit::cols ( ) const

virtual

Reimplemented from AbstractLinAlgPack::MatrixBase.

Definition at line 254 of file ConstrainedOptPack_MatrixVarReductImplicit.cpp.

const VectorSpace & ConstrainedOptPack::MatrixVarReductImplicit::space_cols ( ) const

virtual

Implements AbstractLinAlgPack::MatrixBase.

Definition at line 261 of file ConstrainedOptPack_MatrixVarReductImplicit.cpp.

const VectorSpace & ConstrainedOptPack::MatrixVarReductImplicit::space_rows ( ) const

virtual

Implements AbstractLinAlgPack::MatrixBase.

Definition at line 267 of file ConstrainedOptPack_MatrixVarReductImplicit.cpp.

MatrixOp & ConstrainedOptPack::MatrixVarReductImplicit::operator= ( const MatrixOp & M )

Definition at line 273 of file ConstrainedOptPack_MatrixVarReductImplicit.cpp.

std::ostream & ConstrainedOptPack::MatrixVarReductImplicit::output ( std::ostream & o ) const

virtual

Reimplemented from AbstractLinAlgPack::MatrixOp.

Definition at line 280 of file ConstrainedOptPack_MatrixVarReductImplicit.cpp.

void ConstrainedOptPack::MatrixVarReductImplicit::Vp_StMtV	(	VectorMutable *	v_lhs,
		value_type	alpha,
		BLAS_Cpp::Transp	trans_rhs1,
		const Vector &	v_rhs2,
		value_type	beta
	)		const

Definition at line 289 of file ConstrainedOptPack_MatrixVarReductImplicit.cpp.

void ConstrainedOptPack::MatrixVarReductImplicit::Vp_StMtV	(	VectorMutable *	v_lhs,
		value_type	alpha,
		BLAS_Cpp::Transp	trans_rhs1,
		const SpVectorSlice &	sv_rhs2,
		value_type	beta
	)		const

Definition at line 300 of file ConstrainedOptPack_MatrixVarReductImplicit.cpp.

void ConstrainedOptPack::MatrixVarReductImplicit::Vp_StPtMtV	(	VectorMutable *	v_lhs,
		value_type	alpha,
		const GenPermMatrixSlice &	P_rhs1,
		BLAS_Cpp::Transp	P_rhs1_trans,
		BLAS_Cpp::Transp	M_rhs2_trans,
		const Vector &	v_rhs3,
		value_type	beta
	)		const

Definition at line 358 of file ConstrainedOptPack_MatrixVarReductImplicit.cpp.

void ConstrainedOptPack::MatrixVarReductImplicit::Vp_StPtMtV	(	VectorMutable *	v_lhs,
		value_type	alpha,
		const GenPermMatrixSlice &	P_rhs1,
		BLAS_Cpp::Transp	P_rhs1_trans,
		BLAS_Cpp::Transp	M_rhs2_trans,
		const SpVectorSlice &	sv_rhs3,
		value_type	beta
	)		const